[math]p=\frac{h}{\lambda}[/math]

 

Where does the direction of the momentum come from? Is the wavelength a vector?

Nope. But why do you think that p is a vector?

Nope. But why do you think that p is a vector?

[math]\vec{F}t={\Delta}p[/math]

 

A constant times a vector yields a vector, iirc.

That's a different equation. What guarantees that the two p are the same? And what guarantees that delta-p is the same as p? Or to make things simple: the p in your OP is the magnitude of the momentum.

 

Bottom line: "p" is just a letter, not a physical entity. What it stands for depends on the context (there's rumors about chemists in physics exams who plug in 298 K when calculating an angular frequency via [math] 2\pi / T [/math]).

So, where does the direction come from? Momentum IS a vector.

Then the p in the equation you gave is not the momentum but its magnitude, simple as that (it's only a letter "p"). I don't know how to answer your question. Where does the direction of velocity come from? (comment: in a more formal approach to physics, momentum indeed inherits its vectorial nature directly from velocity)

 

In case that helps you, here's a two equations relating momentum to other vectorial entities: [math]\vec p = m \vec v[/math], [math] \vec p = \hbar \vec k[/math]. The 2nd comes relatively close to your original equation since it also relates momentum to properties of a wave (k is the so-called wave-vector).

Edited October 19, 201015 yr by timo